The Limiting Sum of a Geometric Series (HSC SSCE Mathematics Advanced): Quizzes

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The Limiting Sum of a Geometric Series
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For which condition does a geometric series have a limiting sum?

r<1|r| < 1

Find SS_{\infty} for the series 12+4+43+12 + 4 + \frac{4}{3} + \cdots

1818

What is SS_{\infty} for 248+8324 - 8 + \frac{8}{3} - \cdots?

1818

Which series converges to a limiting sum?

2+1+12+2 + 1 + \frac{1}{2} + \cdots

A GP has first term 1515 and S=20S_{\infty} = 20. Find rr.

14\frac{1}{4}

For what values of xx does 1+(x3)+(x3)2+1 + (x-3) + (x-3)^2 + \cdots converge?

2<x<42 < x < 4

What is the limiting sum of 18+6+2+18 + 6 + 2 + \cdots?

2727

As nn \to \infty, what happens to (12)n(\frac{1}{2})^n?

Approaches 0

What happens when r1|r| \geq 1 in a geometric series?

Series does not converge

If a=8a = 8, r=14r = \frac{1}{4}, what is SS_{\infty}?

323\frac{32}{3}

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